Question: Reading Domain and Range from a Table
Each row below keeps an input and its output together.
Input $x$ Output $y$
$-2$ $6$
$1$ $6$
$1$ $0$
$5$ $-4$
For example, the third row represents $(1, 0)$: input $1$ is paired with output $0$. A table and a list of ordered pairs can describe the same relation.
The domain records which inputs occur. The range records which outputs occur.
Domain = ${-2, 1, 5}$
Range = ${-4, 0, 6}$
Input $1$ appears in two rows, but it is still just one available input. Output $6$ also appears
1. **State the problem:** We are given a table of input-output pairs and need to find the domain and range.
2. **Understand domain and range:**
- The **domain** is the set of all unique input values $x$.
- The **range** is the set of all unique output values $y$.
3. **List the input-output pairs:**
$(-2, 6), (1, 6), (1, 0), (5, -4)$
4. **Find the domain:**
- Inputs are $-2, 1, 1, 5$
- Unique inputs are $\{-2, 1, 5\}$
5. **Find the range:**
- Outputs are $6, 6, 0, -4$
- Unique outputs are $\{-4, 0, 6\}$
6. **Explain duplicates:**
- Even though input $1$ appears twice, it counts once in the domain.
- Output $6$ appears twice but counts once in the range.
7. **Final answer:**
- Domain $= \{-2, 1, 5\}$
- Range $= \{-4, 0, 6\}$